1. -What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities

2. 2 is the greatest exponent: there is a quadratic term. The function is consists of three parts: quadratic, linear and a constant term. Parabola = Graph of the function f(x) = ax² + bx + c (a should not be zero in order to have quadratic term) REVIEW

3. WHAT WE WANT TO ACHIEVE IS… 1.YOU KNOW WHAT ARE QUADRATIC INEQUALITIES. 2.YOU CAN GRAPH QUADRATIC INEQUALITIES IN TWO VARIABLES. 3. YOU CAN SOLVE QUADRATIC INEQUALITIES IN ONE VARIABLE. 4. YOU CAN SOLVE WORD QUESTIONS AND MAKE APPROPRIATE EXPRESSION WITH THE GIVEN CONDITION.

4. GRAPH/SOLVE QUADRATIC INEQUALITIES IN… Two variables One variable

5. FIRST, Two variables

6. 1. HOW TO GRAPH

7. It is similar with quadratic function… If the question asks you to graph y>2x²+4x-1, graph the related function which is y=2x²+4x-1 BUT you have to consider about the parabola → solid or dotted? STEP 1: Graph the related function

8. If the equation has the ≥ or ≤ ‘y≥2x²+4x-1’, it is solid line. (greater/less than or equal to – solid) If the equation has the ‘y>2x²+4x-1’, it is dotted line. (greater/less than -dotted)

9. Solid for y≥2x²+4x-1 Dotted for y>2x²+4x-1

10. You have to test a point to decide where to shade… Pick a point that is not on the parabola and substitute to the function! ex) y>2x²+4x-1 0>2·0²+4·0-1 → ? 0> -1 → O So, (0,0) is a solution of the inequality. STEP 2: Decide where to shade

11. Shade the right region! Since (0,0) IS the solution of the function, shade the place that contains the point. If the point you chose is NOT the solution, you should shade the place that does not contain the point. STEP 3: Shade

12. y≥2x²+4x-1 y>2x²+4x-1

13. Graphing Quadratic Inequalities y=x 2 +4x+2 Equation – only includes the points on the graph (the u shape)

14. y>x 2 +4x+2 –inequality – only includes the points inside the u-shape Dotted Line

15. y<x 2 +4x+2 – inequality – only includes the points outside the parabola Dotted Line

16. y≤x 2 +4x+2 – inequality – both outside and on the parabola Solid Line

17. y≥x 2 +4x+2 inequality – both inside and on the parabola Solid Line

18. A system – where they overlap y≥2x 2 and y<-x 2 +1 Solid Line Dotted Line

19. Try graphing the system